fix(providers): register omo in the runtime lists the type system cannot see

[devswha]

Follow-up to #39. Adding omo to the type unions was not enough: three runtime lookups were left behind, so the provider typechecked, passed 917 tests, went green in CI, and behaved wrongly at every layer.

What was broken

1. omo read gjc's transcripts.

const agentRoot = this.provider === 'omp'
  ? path.join(os.homedir(), '.omp', 'agent')
  : path.join(os.homedir(), '.gjc', 'agent');   // omo lands here

A ternary routes a new union member into its else branch with no type error. Result: 632 gjc sessions indexed as omo, and none of omo's own 5 transcripts ever read.

omo rows: 632 | pointing outside ~/.omo: 632
  e.g. /home/devswha/.gjc/agent/sessions/-workspace-oh-my-docs/…jsonl

2. omo never appeared in the sidebar. Two Array.includes allowlists in useExternalCliSessions dropped it after the backend had correctly reported "kind":"omo".

3. omo replies never refreshed. Its transcript root was missing from PROVIDER_WATCH_PATHS, so the startup scan indexed sessions that no watcher ever updated — sends worked, responses never appeared.

Fix

Root and title lookups become exhaustive Record<PiTranscriptProvider, …>, so the next provider is a compile error rather than a silent fallthrough. The remaining allowlists get omo wherever omp already appears: external spawn (supportedClis), completion identity, event-driven notifications, and the notification label map (omo showed as "Assistant").

Also replaces the placeholder logo with the official oh-my-openagent/.github/assets/omo-icon-light.svg.

Regression lock

pi-transcript-roots.test.ts asserts each pi provider resolves to its own ~/.<provider>/agent and that no two share a root. Verified by mutation: pointing omo back at .gjc fails the test.

Verification

After the fix, against real data:

omo rows: 5 | pointing outside ~/.omo: 0
omo transcripts on disk: 5

The 632 mis-attributed rows were purged and the scan markers cleared. Full gate green: typecheck, lint, identity, server, client.

Note for reviewers

All three defects share one shape — correct types, wrong runtime list. The compiler enumerated the 12 exhaustive Records that needed omo and caught none of these, because Array.includes and ? : are invisible to it. Worth remembering when the next provider lands.